Question

You have total coins for a total of $. . You only have quarters and dimes. Let represent the number of quarters and represent the number of dimes.

Answer 1

`Quarters = 41`

`Dimes = 18`

Explanation:

Given

`Coins = 59`

`Worth = \$12.05`

`d = dimes`

`q = quarters`

Required

The number of each coin

The total coins can be represented as:

`d + q = 59`

`1\ quarter = \$0.25 \\ 1\ dime = \$0.10`

So, the worth of the coin is:

`0.25q + 0.10d = 12.05`

The equations to solve are:

`0.25q + 0.10d = 12.05`

`d + q = 59`

Make d the subject in:
`d + q = 59`

`d =59 - q`

Substitute
`d =59 - q` in
`0.25q + 0.10d = 12.05`

`0.25q + 0.10(59 - q) = 12.05`

`0.25q + 5.9 - 0.10q = 12.05`

Collect like terms

`0.25q - 0.10q = 12.05 - 5.9`

`0.15q = 6.15`

Solve for q

`q=(6.15)/(0.15)`

`q=41`

Substitute
`q=41` in
`d =59 - q`

`d = 59 - 41`

`d = 18`

So:

`Quarters = 41`

`Dimes = 18`